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Clifford Algebra to Geometric Calculus: A Unified Language for Mathematics and Physics
1 / Geometric Algebra.- 1-1. Axioms, Definitions and Identities.- 1-2. Vector Spaces, Pseudoscalars and Projections.- 1-3. Frames and Matrices.- 1-4. Alternating Forms and Determinants.- 1-5.Expand
The Hyperbolic Number Plane
INTRODUCTION. The complex numbers were grudgingly accepted by Renaissance mathematicians because of their utility in solving the cubic equation. Whereas the complex numbers were discovered primarilyExpand
Geometric Algebra with Applications in Science and Engineering
Advances in Geometric Algebra Computing Lie Algebras and Geometric Algebra, Geometric Filtering, Interpolation, Optimization Geometric Algebra of Computer Vision Neural and Quatum Computing GeometricExpand
Simplicial calculus with Geometric Algebra
We construct geometric calculus on an oriented k-surface embedded in Euclidean space by utilizing the notion of an oriented k-surface as the limit set of a sequence of k-chains. This method providesExpand
Relativity in Clifford's Geometric Algebras of Space and Spacetime
Of the various formalisms developed to treat relativistic phenomena, those based on Clifford's geometric algebra are especially well adapted for clear geometric interpretations and computationalExpand
Lectures on Clifford (geometric) algebras and applications
Preface (Rafal Ablamowicz and Garret Sobczyk) * Lecture 1: Introduction to Clifford Algebras (Pertti Lounesto) * 1.1 Introduction * 1.2 Clifford algebra of the Euclidean plane * 1.3 Quaternions * 1.4Expand
Hybrid Matrix Geometric Algebra
A detailed study of the hybrid 2 × 2 matrix geometric algebra M(2,IG) with elements in the 8 dimensional geometric algebra IG=IG3 of Euclidean space, which combines the simplicity of 2× 2 matrices and the clear geometric interpretation of the elements of IG. Expand
Clifford Geometric Algebras in Multilinear Algebra and Non-Euclidean Geometries
Given a quadratic form on a vector space, the geometric algebra of the corresponding pseudo-euclidean space is defined in terms of a simple set of rules which characterizes the geometric product ofExpand
Conformal Mappings in Geometric Algebra
I n 1878 William Kingdon Clifford wrote down the rules for his geometric algebra, also known as Clifford algebra. We argue in this paper that in doing so he laid down the groundwork that isExpand